On the bounded approximation property on subspaces of lp when 0 < p < 1 and related issues

被引：4
|
作者：
Cabello Sanchez, Felix [1 ]
Castillo, Jesus M. F. [1 ]
Moreno, Yolanda [2 ]
机构：
[1] Univ Extremadura, Inst Matemat, Ave Elvas S-N, E-06071 Badajoz, Spain
[2] Univ Extremadura, Inst Matemat, Escuela Politecn, Ave Elvas S-N, E-06071 Caceres, Spain
来源：
FORUM MATHEMATICUM | 2019年 / 31卷 / 06期
关键词：
Bounded approximation property; quasi-Banach space; complementably universal; Fraisse limit; BANACH-SPACES; UNIVERSAL BASES;
D O I：
10.1515/forum-2018-0174
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper studies the bounded approximation property (BAP) in quasi-Banach spaces. In the first part of the paper, we show that the kernel of any surjective operator l(p) -> X has the BAP when X has it and 0 < p <= 1, which is an analogue of the corresponding result of Lusky for Banach spaces. We then obtain and study nonlocally convex versions of the Kadec-Pelczyfisld-Wojtaszczyk complementably universal spaces for Banach spaces with the BAP.
引用
收藏
页码：1533 / 1556
页数：24
相关论文
共 50 条
  • [1] Embedding subspaces of Lp into lpN, 0 &lt; p &lt; 1
    Schechtman, G
    Zvavitch, A
    MATHEMATISCHE NACHRICHTEN, 2001, 227 : 133 - 142
  • [2] Haar approximation from within for Lp(Rd), 0 &lt; p &lt; 1
    Benedetto, John J.
    Njeunje, Franck Olivier Ndjakou
    SAMPLING THEORY SIGNAL PROCESSING AND DATA ANALYSIS, 2021, 19 (01):
  • [3] Adaptive Lp (0 &lt; p &lt; 1) Regularization: Oracle Property and Applications
    Shi, Yunxiao
    He, Xiangnan
    Wu, Han
    Jin, Zhong-Xiao
    Lu, Wenlian
    NEURAL INFORMATION PROCESSING, ICONIP 2017, PT I, 2017, 10634 : 13 - 23
  • [4] SPECTRAL SUBSPACES OF Lp FOR p &lt; 1
    Aleksandrov, A. B.
    ST PETERSBURG MATHEMATICAL JOURNAL, 2008, 19 (03) : 327 - 374
  • [5] Approximation of Fourier series in terms of functions in Lp Spaces for 0 &lt; p &lt; 1
    Aboud, Sahab Mohsen
    Bhaya, Eman Samir
    INTERNATIONAL JOURNAL OF NONLINEAR ANALYSIS AND APPLICATIONS, 2021, 12 (02): : 897 - 911
  • [6] A note on the embedding of subspaces of Lp into lrN, 0&lt;r&lt;1, r≤p&lt;2
    Pena, A
    MATHEMATISCHE NACHRICHTEN, 1998, 189 : 195 - 207
  • [7] The Lp Minkowski problem for polytopes for 0 &lt; p &lt; 1
    Zhu, Guangxian
    JOURNAL OF FUNCTIONAL ANALYSIS, 2015, 269 (04) : 1070 - 1094
  • [8] On the Lp torsional Minkowski problem for 0 &lt; p &lt; 1
    Hu, Jinrong
    Liu, Jiaqian
    ADVANCES IN APPLIED MATHEMATICS, 2021, 128
  • [9] The Lp-mixed quermassintegrals for 0 &lt; p &lt; 1
    Zhao, Chang-Jian
    Bencze, Mihaly
    ACTA UNIVERSITATIS SAPIENTIAE-MATHEMATICA, 2021, 13 (02) : 519 - 528
  • [10] Banach spaces embedding isometrically into Lp when 0&lt;p&lt;1
    Kalton, NJ
    Koldobsky, A
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2004, 132 (01) : 67 - 76
12345